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Refinements of Rationalizability for Normal-Form Games

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  • Herings, P.J.J.

    (Tilburg University, Center For Economic Research)

  • Vannetelbosch, V.

Abstract

In normal-form games, rationalizability (Bernheim [3], Pearce [11]) on its own fails to exclude some very implausible strategy choices. Three main refinements of ra- tionalizability have been proposed in the literature: cautious, perfect, and proper rationalizability. Nevertheless, some of these refinements also fail to eliminate un- reasonable outcomes and suffer from several drawbacks. Therefore, we introduce the trembling-hand rationalizability concept, where the players’ actions have to be best responses also against perturbed conjectures. We also propose another refinement: weakly perfect rationalizability, where players’ actions that are not best responses are only played with a very small probability. We show the relationship between perfect rationalizability and weakly perfect ratio- nalizability as well as the relationship between proper rationalizability and weakly perfect rationalizability : weakly perfect rationalizability is a weaker refinement than both perfect and proper rationalizability. Moreover, in two-player games it holds that weakly perfect rationalizability is a weaker refinement than trembling-hand rational- izability. The other relationships between the various refinements are illustrated by means of examples. For the relationship between any other two refinements we give examples showing that the remaining set of strategies corresponding to the first re- finement can be either smaller or larger than the one corresponding to the second refinement.
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Suggested Citation

  • Herings, P.J.J. & Vannetelbosch, V., 1997. "Refinements of Rationalizability for Normal-Form Games," Discussion Paper 1997-03, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:7dc795b0-6250-4c14-828a-d05587d62a81
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    References listed on IDEAS

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    1. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    3. Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 13-25.
    4. Ben-Porath, Elchanan & Dekel, Eddie, 1992. "Signaling future actions and the potential for sacrifice," Journal of Economic Theory, Elsevier, vol. 57(1), pages 36-51.
    5. Vannetelbosch, Vincent J., 1996. "Refinements of Rationalizability for Normal-Form Games: The Main Ideas," LIDAM Discussion Papers IRES 1996012, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    6. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
    7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
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    Cited by:

    1. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    2. P. Jean-Jacques Herings & Ana Mauleon & Vincent J. Vannetelbosch, 2004. "Fuzzy play, matching devices and coordination failures," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 519-531, August.
    3. Kool, C.J.M. & Thornton, D., 2000. "The expectations theory and the founding of the fed: another look at the evidence," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 2000. "The equivalence of the Dekel-Fudenberg iterative procedure and weakly perfect rationalizability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 677-687.
    5. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent J., 2004. "Rationalizability for social environments," Games and Economic Behavior, Elsevier, vol. 49(1), pages 135-156, October.
    6. Mauleon, Ana & Vannetelbosch, Vincent, 2004. "Bargaining with endogenous deadlines," Journal of Economic Behavior & Organization, Elsevier, vol. 54(3), pages 321-335, July.
    7. Ana Mauleon & Vincent Vannetelbosch, 2003. "Farsightedness and Cautiousness in Coalition Formation," Working Papers 2003.52, Fondazione Eni Enrico Mattei.
    8. Herings, P.J.J. & Mauleon, A. & Vannetelbosch, V., 2000. "Social rationalizability," Research Memorandum 017, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Goossens, J.H.M. & van Hoesel, C.P.M. & Kroon, L.G., 2002. "On solving multi-type line planning problems," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    11. Gilles Grandjean & Ana Mauleon & Vincent Vannetelbosch, 2017. "Strongly rational sets for normal-form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 35-46, April.
    12. Vannetelbosch, Vincent J., 1996. "Bargaining with an Endogenous Deadline," LIDAM Discussion Papers IRES 1996011, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    13. Asheim,G.B., 1999. "Proper consistency," Memorandum 31/1999, Oslo University, Department of Economics.
    14. Vincent Vannetelbosch, 1999. "Alternating-Offer Bargaining and Common Knowledge of Rationality," Theory and Decision, Springer, vol. 47(2), pages 111-138, October.
    15. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    16. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    17. Xiao Luo & Xuewen Qian & Yang Sun, 2021. "The algebraic geometry of perfect and sequential equilibrium: an extension," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 579-601, March.
    18. A. Mauleon & V. Vannetelbosch, 2000. "Coalitional Negotiation with Monitoring," THEMA Working Papers 2000-35, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    19. MAULEON, Ana & VANNETELBOSCH, Vincent, 1999. "Coalitional negotiation," LIDAM Discussion Papers CORE 1999020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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    More about this item

    Keywords

    rationalizability; refinements;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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